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On line solution of multivariate equations：
    First set the elements of the equation (i.e. the number of unknowns), then click the "Next" button to enter the coefficients of each element of the equation set, and click the "Next" button to obtain the solution of the equation set.
    Note that the coefficients of each element of the equation system can only be numbers, not algebraic expressions (including mathematical functions).
    Current location：Equations > Multivariate equations > Answer
detailed information：
The input equation set is:
 A + B + C + D = 
83683
50
    (1)
 
54
5
A + 
83
10
B + 
29
5
C + E = 
51049
5
    (2)
 
14
5
A + 
29
5
B + 
39
5
C + 
69
5
D -1E = 
61929
5
    (3)
 
14
5
B + 5C + 
54
5
D -1E = 
39334
5
    (4)
- 
14
5
A + 
14
5
C + 
44
5
D -1E = 
18414
5
    (5)
Question solving process:

Multiply both sides of equation (1) by 54
Divide the two sides of equation (1) by 5, the equation can be obtained:
         
54
5
A + 
54
5
B + 
54
5
C + 
54
5
D = 
2259441
125
    (6)
, then subtract both sides of equation (6) from both sides of equation (2), the equations are reduced to:
 A + B + C + D = 
83683
50
    (1)
- 
5
2
B -5C - 
54
5
D + E = - 
983216
125
    (2)
 
14
5
A + 
29
5
B + 
39
5
C + 
69
5
D -1E = 
61929
5
    (3)
 
14
5
B + 5C + 
54
5
D -1E = 
39334
5
    (4)
- 
14
5
A + 
14
5
C + 
44
5
D -1E = 
18414
5
    (5)

Multiply both sides of equation (1) by 14
Divide the two sides of equation (1) by 5, the equation can be obtained:
         
14
5
A + 
14
5
B + 
14
5
C + 
14
5
D = 
585781
125
    (7)
, then subtract both sides of equation (7) from both sides of equation (3), the equations are reduced to:
 A + B + C + D = 
83683
50
    (1)
- 
5
2
B -5C - 
54
5
D + E = - 
983216
125
    (2)
 3B + 5C + 11D -1E = 
962444
125
    (3)
 
14
5
B + 5C + 
54
5
D -1E = 
39334
5
    (4)
- 
14
5
A + 
14
5
C + 
44
5
D -1E = 
18414
5
    (5)

Multiply both sides of equation (1) by 14
Divide the two sides of equation (1) by 5, the equation can be obtained:
         
14
5
A + 
14
5
B + 
14
5
C + 
14
5
D = 
585781
125
    (8)
, then add the two sides of equation (8) to both sides of equation (5), the equations are reduced to:
 A + B + C + D = 
83683
50
    (1)
- 
5
2
B -5C - 
54
5
D + E = - 
983216
125
    (2)
 3B + 5C + 11D -1E = 
962444
125
    (3)
 
14
5
B + 5C + 
54
5
D -1E = 
39334
5
    (4)
 
14
5
B + 
28
5
C + 
58
5
D -1E = 
1046131
125
    (5)

Multiply both sides of equation (2) by 6
Divide the two sides of equation (2) by 5, the equation can be obtained:
        -3B -6C - 
324
25
D + 
6
5
E = - 
5899296
625
    (9)
, then add the two sides of equation (9) to both sides of equation (3), the equations are reduced to:
 A + B + C + D = 
83683
50
    (1)
- 
5
2
B -5C - 
54
5
D + E = - 
983216
125
    (2)
-1C - 
49
25
D + 
1
5
E = - 
1087076
625
    (3)
 
14
5
B + 5C + 
54
5
D -1E = 
39334
5
    (4)
 
14
5
B + 
28
5
C + 
58
5
D -1E = 
1046131
125
    (5)

Multiply both sides of equation (2) by 28
Divide the two sides of equation (2) by 25, the equation can be obtained:
        - 
14
5
B - 
28
5
C - 
1512
125
D + 
28
25
E = - 
27530048
3125
    (10)
, then add the two sides of equation (10) to both sides of equation (4), the equations are reduced to:
 A + B + C + D = 
83683
50
    (1)
- 
5
2
B -5C - 
54
5
D + E = - 
983216
125
    (2)
-1C - 
49
25
D + 
1
5
E = - 
1087076
625
    (3)
- 
3
5
C - 
162
125
D + 
3
25
E = - 
2946298
3125
    (4)
 
14
5
B + 
28
5
C + 
58
5
D -1E = 
1046131
125
    (5)

Multiply both sides of equation (2) by 28
Divide the two sides of equation (2) by 25, the equation can be obtained:
        - 
14
5
B - 
28
5
C - 
1512
125
D + 
28
25
E = - 
27530048
3125
    (11)
, then add the two sides of equation (11) to both sides of equation (5), the equations are reduced to:
 A + B + C + D = 
83683
50
    (1)
- 
5
2
B -5C - 
54
5
D + E = - 
983216
125
    (2)
-1C - 
49
25
D + 
1
5
E = - 
1087076
625
    (3)
- 
3
5
C - 
162
125
D + 
3
25
E = - 
2946298
3125
    (4)
- 
62
125
D + 
3
25
E = - 
1376773
3125
    (5)

Multiply both sides of equation (3) by 3
Divide the two sides of equation (3) by 5, the equation can be obtained:
        - 
3
5
C - 
147
125
D + 
3
25
E = - 
3261228
3125
    (12)
, then subtract both sides of equation (12) from both sides of equation (4), the equations are reduced to:
 A + B + C + D = 
83683
50
    (1)
- 
5
2
B -5C - 
54
5
D + E = - 
983216
125
    (2)
-1C - 
49
25
D + 
1
5
E = - 
1087076
625
    (3)
- 
3
25
D = 
62986
625
    (4)
- 
62
125
D + 
3
25
E = - 
1376773
3125
    (5)

Multiply both sides of equation (4) by 62
Divide the two sides of equation (4) by 15, the equation can be obtained:
        - 
62
125
D = 
3905132
9375
    (13)
, then subtract both sides of equation (13) from both sides of equation (5), the equations are reduced to:
 A + B + C + D = 
83683
50
    (1)
- 
5
2
B -5C - 
54
5
D + E = - 
983216
125
    (2)
-1C - 
49
25
D + 
1
5
E = - 
1087076
625
    (3)
- 
3
25
D = 
62986
625
    (4)
 
3
25
E = - 
8035451
9375
    (5)

Multiply both sides of equation (5) by 5
Divide both sides of equation (5) by 3, get the equation：
         
1
5
E = - 
8035451
5625
    (14)
, then subtract both sides of equation (14) from both sides of equation (3), get the equation：
 A + B + C + D = 
83683
50
    (1)
- 
5
2
B -5C - 
54
5
D + E = - 
983216
125
    (2)
-1C - 
49
25
D = - 
1748233
5625
    (3)
- 
3
25
D = 
62986
625
    (4)
 
3
25
E = - 
8035451
9375
    (5)

Multiply both sides of equation (5) by 25
Divide both sides of equation (5) by 3, get the equation：
         E = - 
8035451
1125
    (15)
, then subtract both sides of equation (15) from both sides of equation (2), get the equation：
 A + B + C + D = 
83683
50
    (1)
- 
5
2
B -5C - 
54
5
D = - 
813493
1125
    (2)
-1C - 
49
25
D = - 
1748233
5625
    (3)
- 
3
25
D = 
62986
625
    (4)
 
3
25
E = - 
8035451
9375
    (5)

Multiply both sides of equation (4) by 49
Divide both sides of equation (4) by 3, get the equation：
        - 
49
25
D = 
3086314
1875
    (16)
, then subtract both sides of equation (16) from both sides of equation (3), get the equation：
 A + B + C + D = 
83683
50
    (1)
- 
5
2
B -5C - 
54
5
D = - 
813493
1125
    (2)
-1C = - 
440287
225
    (3)
- 
3
25
D = 
62986
625
    (4)
 E = - 
8035451
1125
    (5)

Multiply both sides of equation (4) by 90, get the equation：
        - 
54
5
D = 
1133748
125
    (17)
, then subtract both sides of equation (17) from both sides of equation (2), get the equation：
 A + B + C + D = 
83683
50
    (1)
- 
5
2
B -5C = - 
440689
45
    (2)
-1C = - 
440287
225
    (3)
- 
3
25
D = 
62986
625
    (4)
 E = - 
8035451
1125
    (5)

Multiply both sides of equation (4) by 25
Divide both sides of equation (4) by 3, get the equation：
        -1D = 
62986
75
    (18)
, then add the two sides of equation (18) to both sides of equation (1), get the equation：
 A + B + C = 
377021
150
    (1)
- 
5
2
B -5C = - 
440689
45
    (2)
-1C = - 
440287
225
    (3)
- 
3
25
D = 
62986
625
    (4)
 E = - 
8035451
1125
    (5)

Multiply both sides of equation (3) by 5, get the equation：
        -5C = - 
440287
45
    (19)
, then subtract both sides of equation (19) from both sides of equation (2), get the equation：
 A + B + C = 
377021
150
    (1)
- 
5
2
B = - 
134
15
    (2)
-1C = - 
440287
225
    (3)
 D = - 
62986
75
    (4)
 E = - 
8035451
1125
    (5)

Add both sides of equation (3) to both sides of equation (1), get the equation：
 A + B = 
250489
450
    (1)
- 
5
2
B = - 
134
15
    (2)
-1C = - 
440287
225
    (3)
 D = - 
62986
75
    (4)
 E = - 
8035451
1125
    (5)

Multiply both sides of equation (2) by 2
Divide both sides of equation (2) by 5, get the equation：
        -1B = - 
268
75
    (20)
, then add the two sides of equation (20) to both sides of equation (1), get the equation：
 A = 
248881
450
    (1)
- 
5
2
B = - 
134
15
    (2)
 C = 
440287
225
    (3)
 D = - 
62986
75
    (4)
 E = - 
8035451
1125
    (5)

The coefficient of the unknown number is reduced to 1, and the equations are reduced to：
 A = 
248881
450
    (1)
 B = 
268
75
    (2)
 C = 
440287
225
    (3)
 D = - 
62986
75
    (4)
 E = - 
8035451
1125
    (5)


Therefore, the solution of the equation set is:
A = 
248881
450
B = 
268
75
C = 
440287
225
D = - 
62986
75
E = - 
8035451
1125


Convert the solution of the equation set to decimals:
A = 553.068889
B = 3.573333
C = 1956.831111
D = -839.813333
E = -7142.623111

解方程组的详细方法请参阅：《多元一次方程组的解法》
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